The distance S an object travels under the influence of gravity in time t seconds is given by S(t) = 1/2.gt^2 +at +bt where, (g is the acceleration due to gravity), a, b are constants. Check if the function S (t )is one-one type of function (injection/injective)
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Answer:
In an injective function each and every element in the domain should have a unique image/value in in the range.
In this case only t is independent value and for this equation to be injective for every value of t there should be a unique value of S.
To check we will differentiate the function and see if it is continuously decreasing or increasing.
Step 1
Differentiating the given function with respect to time.
gt+a+b
Case 1
If a and b are positive the function is continuously increasing, therefore it is an injective function.
Case 2
If a and b are negative the function is continuously decreasing till gt is less than a+b and increases after that , therefore it is not an injective function in this case.
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